A Study of LY3090106 in Healthy Participants and Participants With Rheumatoid Arthritis (RA)

Inclusion Criteria for Healthy Participants: * Males or non-pregnant females age 18 to 65 years * Body Mass Index (BMI) of 18.5 to 32.0 kilograms per meter squared (kg/m\^2) Inclusion Criteria for Participants for RA: * Diagnosis of at least mildly active adult-onset RA * Positive anti-citrullinated protein (ACPA) antibodies or rheumatoid factor * Regular use of MTX for at least 12 weeks and at a stable dose (10 to 25 mg/week) for at least 4 weeks prior to baseline * American College of Rheumatology (ACR) Functional Class I, II or III Exclusion Criteria for Healthy Participants: * Have received biologic agents within 3 months or 5 half-lives * Have surgery within 12 weeks prior to screening * Known history of human immunodeficiency virus (HIV infection and/or positive human HIV antibodies) * Have evidence of, or test positive for, hepatitis C virus or hepatitis B virus * Have evidence of active infection or fever * Have donated greater than 500 mL blood within 30 days prior to screening * Smoke greater than 10 cigarettes/day or equivalent * Have received live vaccine within 1 month of screening * Have a history of allergy to monoclonal antibodies or severe drug allergies Exclusion Criteria for Participants with RA: * Have received prior or current treatment with biologic RA therapies * Have received a live vaccine 28 days prior to screening or intend to receive a live vaccine during the course of the study * Hemoglobin \< 10 grams per deciliter (g/dL), platelet count \< 100,000 cells/microliter (uL), total white blood cell count \< 3000 cells/uL, neutrophil count \< 2000 cells/uL, or lymphocyte count \< 500 cells/uL * Aspartate transaminase (AST) \> 1.5 x upper limit or the normal range (ULN), alanine transamine (ALT) \> 1.5 x ULN, creatinine \> 1.5 mg/dL (114 micromoles/liter \[uMol/L\]) * Treatment with \> 10 mg/day or unstable dose of oral prednisone or equivalent within 28 days of baseline * Have required an increase in dose or a new prescription of narcotic within 28 days prior to randomization * Have received any parenteral corticosteroids within 28 days before screening * Treatment with any oral disease-modifying anti-rheumatic drugs (DMARDs) other than MTX within 4 weeks prior to baseline * Any neurological, psychiatric, vascular, or system disorder that could also affect the evaluation of disease activity assessments. Anemia of chronic disease is allowed if hemoglobin \> 10 g/dL * Have rheumatic or systemic autoimmune disease other than RA or significant active systemic involvement secondary to RA. Participants with secondary Sjogren's syndrome are eligible. * Uncontrolled arterial hypertension characterized by a confirmed systolic blood pressure of \> 150 mm Hg or diastolic blood pressure \> 90 mm Hg at screening or on day of study drug dosing * Poorly controlled diabetes as defined by glycosylated hemoglobin (HbA1c) \> 8.0% at screening * Known history of human immunodeficiency virus (HIV infection and/or positive human HIV antibodies) * Have evidence of, or test positive for, hepatitis C virus or hepatitis B virus